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 A366767 Array read by antidiagonals, where each row is the counting sequence of a certain type of fixed polyominoids. 25
 1, 0, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 0, 2, 2, 0, 1, 0, 2, 4, 2, 0, 1, 0, 2, 12, 6, 1, 0, 1, 0, 2, 38, 22, 0, 1, 0, 1, 0, 2, 126, 88, 0, 2, 1, 0, 1, 0, 2, 432, 372, 0, 6, 2, 1, 0, 1, 0, 2, 1520, 1628, 0, 19, 6, 4, 3, 0, 1, 0, 2, 5450, 7312, 0, 63, 19, 20, 0, 3 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS See A366766 (corresponding array for free polyominoids) for details. LINKS Table of n, a(n) for n=1..78. Pontus von Brömssen, Python programs that relate row numbers and parameter sets. Wikipedia, Polyominoid. Index entries for sequences related to polyominoes. EXAMPLE Array begins: n\k| 1 2 3 4 5 6 7 8 9 10 11 12 ---+-------------------------------------------------------------------- 1 | 1 0 0 0 0 0 0 0 0 0 0 0 2 | 1 1 1 1 1 1 1 1 1 1 1 1 3 | 2 0 0 0 0 0 0 0 0 0 0 0 4 | 2 2 2 2 2 2 2 2 2 2 2 2 5 | 2 4 12 38 126 432 1520 5450 19820 72892 270536 1011722 6 | 2 6 22 88 372 1628 7312 33466 155446 730534 3466170 16576874 7 | 1 0 0 0 0 0 0 0 0 0 0 0 8 | 1 2 6 19 63 216 760 2725 9910 36446 135268 505861 9 | 1 2 6 19 63 216 760 2725 9910 36446 135268 505861 10 | 1 4 20 110 638 3832 23592 147941 940982 6053180 39299408 257105146 11 | 3 0 0 0 0 0 0 0 0 0 0 0 12 | 3 3 3 3 3 3 3 3 3 3 3 3 CROSSREFS Cf. A366766 (free), A366768. The following table lists some sequences that are rows of the array, together with the corresponding values of D, d, and C (see A366766). Some sequences occur in more than one row. Notation used in the table: X: Allowed connection. -: Not allowed connection (but may occur "by accident" as long as it is not needed for connectedness). .: Not applicable for (D,d) in this row. !: d < D and all connections have h = 0, so these polyominoids live in d < D dimensions only. *: Whether a connection of type (g,h) is allowed or not is independent of h. | | | connections | | | | g:112223 | n | D | d | h:010120 | sequence ----+---+---+-------------+---------- 1 | 1 | 1 | * -..... | A063524 2 | 1 | 1 | * X..... | A000012 3 |!2 | 1 | * --.... | 2*A063524 4 |!2 | 1 | X-.... | 2*A000012 5 | 2 | 1 | -X.... | 2*A001168 6 | 2 | 1 | * XX.... | A096267 7 | 2 | 2 | * -.-... | A063524 8 | 2 | 2 | * X.-... | A001168 9 | 2 | 2 | * -.X... | A001168 10 | 2 | 2 | * X.X... | A006770 11 |!3 | 1 | * --.... | 3*A063524 12 |!3 | 1 | X-.... | 3*A000012 13 | 3 | 1 | -X.... | A365655 14 | 3 | 1 | * XX.... | A365560 15 |!3 | 2 | * ----.. | 3*A063524 16 |!3 | 2 | X---.. | 3*A001168 17 | 3 | 2 | -X--.. | A365655 18 | 3 | 2 | * XX--.. | A075678 19 |!3 | 2 | --X-.. | 3*A001168 20 |!3 | 2 | X-X-.. | 3*A006770 21 | 3 | 2 | -XX-.. | A365996 22 | 3 | 2 | XXX-.. | A365998 23 | 3 | 2 | ---X.. | A366000 24 | 3 | 2 | X--X.. | A366002 25 | 3 | 2 | -X-X.. | A366004 26 | 3 | 2 | XX-X.. | A366006 27 | 3 | 2 | * --XX.. | A365653 28 | 3 | 2 | X-XX.. | A366008 29 | 3 | 2 | -XXX.. | A366010 30 | 3 | 2 | * XXXX.. | A365651 31 | 3 | 3 | * -.-..- | A063524 32 | 3 | 3 | * X.-..- | A001931 33 | 3 | 3 | * -.X..- | A039742 34 | 3 | 3 | * X.X..- | 35 | 3 | 3 | * -.-..X | A039741 36 | 3 | 3 | * X.-..X | 37 | 3 | 3 | * -.X..X | 38 | 3 | 3 | * X.X..X | 39 |!4 | 1 | * --.... | 4*A063524 40 |!4 | 1 | X-.... | 4*A000012 41 | 4 | 1 | -X.... | A366341 42 | 4 | 1 | * XX.... | A365562 43 |!4 | 2 | * -----. | 6*A063524 44 |!4 | 2 | X----. | 6*A001168 45 | 4 | 2 | -X---. | A366339 46 | 4 | 2 | * XX---. | A366335 47 |!4 | 2 | --X--. | 6*A001168 48 |!4 | 2 | X-X--. | 6*A006770 Sequence in context: A357860 A147648 A363879 * A113686 A361414 A193403 Adjacent sequences: A366764 A366765 A366766 * A366768 A366769 A366770 KEYWORD nonn,tabl AUTHOR Pontus von Brömssen, Oct 22 2023 STATUS approved

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Last modified May 22 11:26 EDT 2024. Contains 372745 sequences. (Running on oeis4.)